You both seem to have some major communication issues.

Do you believe she is cheating on you? From what you write, it does not seem to be the case, which she keeps telling you. Yet, you violate her privacy by checking her private messages(!), you talk about her to her sister and family(?!). These are not trustworthy behaviours. In this sense, you are as bad as she is: she speaks badly of you to him but you (and your friend) do the same - you speak badly of her to her friends/family AND you do not have a diagnosis of autism to justify this behaviour (because you use autism as the justification for how *she* functions)

You do seem to have *a lot* of mistrust and question everything, even her low libido, which you take personally.

I agree that this guy might be interested in her sexually (that photo he sent was inappropriate) but it also seems that she is not interested in him sexually and is not flirting with him. It seems she needs someone she can talk to because - in your own words, you are *not* a good listener and she feels that she cannot talk to you.

Couples counselling might help you both hear one another and understand one another (especially with regards to her autism and what that means) because there does not seem to be much trust nor healthy communication in this relationship.